LMTD Calculator (Log Mean Temperature Difference)

How it works

LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂) · counterflow: ΔT₁ = Th,in − Tc,out, ΔT₂ = Th,out − Tc,in · parallel flow: ΔT₁ = Th,in − Tc,in, ΔT₂ = Th,out − Tc,out · Q = U × A × LMTD → A = Q ÷ (U × LMTD) · ε = largest stream ΔT ÷ (Th,in − Tc,in)

The log mean temperature difference is the effective driving temperature difference along a heat exchanger, because the gap between the hot and cold fluids changes from one end to the other. Multiplied by the overall coefficient U and the area A it gives the heat duty Q. Counterflow always gives a larger LMTD than parallel flow for the same temperatures, so it needs less area and can even heat the cold fluid above the hot outlet. For shell-and-tube exchangers with several passes or crossflow, multiply the counterflow LMTD by a correction factor F (usually 0.8–1) from TEMA or textbook charts.

Worked example

Hot oil cooled from 150 °C to 90 °C heats water from 30 °C to 70 °C in counterflow. The end differences are 150 − 70 = 80 °C and 90 − 30 = 60 °C, so LMTD = (80 − 60) ÷ ln(80 ÷ 60) = 69.52 °C (the arithmetic mean would be 70 °C). For a duty of 100 kW and U = 500 W/m²·K the area is 100,000 ÷ (500 × 69.52) = 2.877 m². The same temperatures in parallel flow give LMTD = 55.81 °C and need 24.6% more area. Effectiveness is 60 ÷ 120 = 50%.

Sources: Engineering ToolBox — Log mean temperature difference · Wikipedia — Logarithmic mean temperature difference

Frequently asked questions